Moment of Inertia Calculator
Moment of inertia calculator: find I for a cylinder, sphere, rod or point mass from its mass and radius or length.
Editorial review: Farrow (pseudonym; identity and professional credentials are not disclosed). This page is for educational purposes, not professional advice.
Your inputs
Results update as you type. Nothing you enter leaves your device.
Results
Example with the starting values
These results use the calculator's initial inputs. Change the values above to calculate your own estimate.
Inputs
- Shape
- Solid cylinder or disk (about axis)
- Mass
- 2 kg
- Radius or length
- 0.5 m
Results
- Moment of inertia
- 0.25 kg·m²
How does the Moment of Inertia Calculator work?
Moment of inertia measures how hard it is to change an object's spin. Each shape has a formula, such as I = ½·m·r² for a solid cylinder.
For example, a 2 kg solid cylinder of radius 0.5 m has I = 0.5 × 2 × 0.5² = 0.25 kg·m².
Frequently asked questions
Does the axis of rotation change the answer?
Yes. The same rod has I = ⅟₁₂mL² about its center but ⅓mL² about its end, so pick the matching shape.
What is the moment of inertia?
It is the rotational equivalent of mass: the larger it is, the more torque is needed to change the spin rate.
What are the common formulas?
Solid cylinder ½mr², hollow cylinder mr², solid sphere ⅖mr², thin spherical shell ⅔mr², rod about its center ⅟₁₂mL², rod about its end ⅓mL².
What units is the answer in?
Kilogram square meters (kg·m²) when mass is in kg and length in meters.
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